A — 1: ἐκδικέω
(Strong's #1556 — Verb — ekdikeo — ek-dik-eh'-o )

ek, "from," dike, "justice," i.e., that which proceeds from justice, means (a) "to vindicate a person's right," (b) "to avenge a thing." With the meaning (a), it is used in the parable of the unjust judge, Luke 18:3,5 , of the "vindication" of the rights of the widow; with the meaning (b) it is used in Revelation 6:10; 19:2 , of the act of God in "avenging" the blood of the saints; in 2—Corinthians 10:6 , of the Apostle's readiness to use his apostolic authority in punishing disobedience on the part of his readers; here the RV substitutes "avenge" for the AV, "revenge;" in Romans 12:19 of "avenging" oneself, against which the believer is warned.

Revelation 18:20
B — 1: ἔκδικος
(Strong's #1558 — Adjective — ekdikos — ek'-dik-os )

primarily, "without law," then, "one who exacts a penalty from a person, an avenger, a punisher," is used in Romans 13:4 of a civil authority in the discharge of his function of executing wrath on the evildoer (AV, wrongly, "revenger"); in 1—Thessalonians 4:6 , of God as the avenger of the one who wrongs his brother, here particularly in the matter of adultery.

B — 2: ἐκδίκησις
(Strong's #1557 — Noun Feminine — ekdikesis — ek-dik'-ay-sis )

"vengeance," is used with the verb poieo, "to make," i.e., to avenge, in Luke 18:7,8; Acts 7:24; twice it is used in statements that "vengeance" belongs to God, Romans 12:19; Hebrews 10:30 . In 2—Thessalonians 1:8 it is said of the act of Divine justice which will be meted out to those who know not God and obey not the Gospel, when the Lord comes in flaming fire at His second advent. In the Divine exercise of judgment there is no element of vindictiveness, nothing by way of taking revenge. In Luke 21:22 , it is used of the "days of vengeance" upon the Jewish people; in 1—Peter 2:14 , of civil governors as those who are sent of God "for vengeance on evildoers" (AV, "punishment"); in 2—Corinthians 7:11 , of the "self-avenging" of believers, in their godly sorrow for wrong doing, RV, "avenging," for AV, "revenge." See PUNISHMENT , VENGEANCE.